Causal structure in the presence of sectorial constraints, with application to the quantum switch

Abstract

Existing work on quantum causal structure assumes that one can perform arbitrary operations on the systems of interest. But this condition is often not met. Here, we extend the framework for quantum causal modelling to situations where a system can suffer sectorial constraints, that is, restrictions on the orthogonal subspaces of its Hilbert space that may be mapped to one another. Our framework (a) proves that a number of different intuitions about causal relations turn out to be equivalent; (b) shows that quantum causal structures in the presence of sectorial constraints can be represented with a directed graph; and (c) defines a fine-graining of the causal structure in which the individual sectors of a system bear causal relations. As an example, we apply our framework to purported photonic implementations of the quantum switch to show that while their coarse-grained causal structure is cyclic, their fine-grained causal structure is acyclic. We therefore conclude that these experiments realize indefinite causal order only in a weak sense. Notably, this is the first argument to this effect that is not rooted in the assumption that the causal relata must be localized in spacetime.

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Cited by in corpus (19)

• Experimental Aspects of Indefinite Causal Order in Quantum Mechanics
• Higher-order Process Matrix Tomography of a passively-stable Quantum SWITCH
• Identification is Pointless: Quantum Coordinates, Localisation of Events, and the Quantum Hole Argument
• Experimental demonstration of input-output indefiniteness in a single quantum device
• Quantum metrology in the finite-sample regime
• Existence of processes violating causal inequalities on time-delocalised subsystems
• Security of differential phase shift QKD from relativistic principles
• Embedding cyclic information-theoretic structures in acyclic spacetimes: no-go results for indefinite causality
• Fundamental limits for realising quantum processes in spacetime
• Gravitational quantum switch on a superposition of spherical shells
• Equivalence Principle in Classical and Quantum Gravity
• Indefinite causal order and quantum coordinates
• Quantum Supermaps are Characterized by Locality
• Consistent circuits for indefinite causal order
• Mapping indefinite causal order processes to composable quantum protocols in a spacetime
• The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications
• Toward an Experimental Device-Independent Verification of Indefinite Causal Order
• What can we do in a symmetry-constrained perspective? The importance of the total charge's status in quantum reference frame frameworks
• Knot invariants and indefinite causal order